Stefan Forcey
Department of Mathematics
The University of Akron
Akron, OH 44325-4002
USA

Michael Strayer
Department of Mathematics
The University of Akron
Akron, OH 44325-4002
USA

Abstract:

In this note we introduce several instructive examples of bijections
found between several different combinatorially defined sequences
ofsets. Each sequence has cardinalities given by the Catalan numbers.
Our results answer some questions posed by R. Stanley in the addendum
to his textbook. We actually discuss two types of bijection, one
defined recursively and the other defined in a more local, relative,
fashion. It is interesting to compare the results of the two.